The logical reasoning capabilities of pre-trained language models have recently received much attention. As one of the vital reasoning paradigms, non-monotonic reasoning refers to the fact that conclusions may be invalidated with new information. Existing work has constructed a non-monotonic inference dataset 𝛿-NLI and explored the performance of language models on it. However, the 𝛿-NLI dataset is entangled with commonsense reasoning. In this paper, we explore the pure non-monotonic reasoning ability of pre-trained language models. We build a non-monotonic reasoning benchmark, named LogicNMR, with explicit default rules and iterative updates. In the experimental part, the performance of popular language models on LogicNMR is explored from the perspectives of accuracy, generalization, proof-based traceability and robustness. The experimental results show that even though the fine-tuned language models achieve an accuracy of more than 94.4% on LogicNMR, they perform unsatisfactorily, with a significant drop, in generalization and proof-based traceability.